Atos ran computers for the Home Office for £62m last year. Photograph: Graham Turner for the Guardian

Ministers have outsourced more than £3bn of public services to Atos, the multinational IT firm whose sponsorship of the Paralympics has prompted a nationwide campaign by disability activists.

A series of parliamentary questions from Labour MP Tom Greatrex reveals the value of contracts with Atos is now more than a third higher than the amount outsourced by the last government. The replies expose how far the reach of the company extends in Whitehall.

The revelations come as the company, which conducts controversial medical assessments for benefit claims on behalf of the government, reaps the benefits of its association with the Olympic and Paralympic movement. City analysts estimate that Atos's work for the London Olympic and Paralympic Games is worth £200m in revenues. They say its sponsorship of the events helps showcase "its technology and project management capabilities".

On Wednesday disabled protesters will deliver a coffin filled with 85 pages of complaints from people and their families who have been told they have to get a job despite suffering from serious impairments. They point out that 1,100 people died last year after failing the test for the new incapacity benefit.

Linda Burnip, the co-founder of Disabled People Against Cuts, which is leading the campaign, said: "The fact is that Atos is getting all the credit for the Paralympics and at the same time it is destroying disabled people's lives through the work capability assessments."

Greatrex has secured a Westminster Hall debate on Atos and the work capability assessments on 4 September.

While 10 government departments have contracts with the company, its most high-profile deal sprang from a Labour pilot project in 2008 to decide whether people were fit to work or eligible for Employment and Support Allowance (ESA). This contract – worth £112m last year – has been extended across the country by the coalition government and been the focus of campaigners' ire.

The company has conducted about 738,000 work capability assessments on benefit claimants in the past financial year. However the assessments have been widely criticised and it has emerged that 40% of people appeal against the decisions – with 38% of those successful. The cost to the taxpayer of the tribunal system alone is £50m, around half of the amount spent on reassessment.

"Despite the huge concerns that have been raised about the way in which the work capability assessment is delivered by Atos, it seems the Tory-led government is happy to increase the value of its contracts with the firm," he said. "Ministers appear to be either unconcerned or unaware of the problems with Atos – both of which reflect badly on the very people who should be doing their job in getting better value for money for the taxpayer, and a fairer assessment for those who have to go through it."

Disabled activists who have campaigned against the medical assessments say they are astonished to learn that this contract is the tip of the iceberg. Atos won three contracts from the Department for International Development worth £270m, including £20m to run a federal public administration reform programme in Nigeria. It also won a £33m contract to run IT for the Highways Agency and ran computers for the Home Office in an arrangement which cost the taxpayer £62m last year.

Ministers have been impressed with Atos's performance – the company was the first IT firm to sign a new "memorandum of understanding" after the Cabinet Office minister, Francis Maude, redesigned Labour contracts he considered too favourable to the private sector. In a vote of confidence in the company this month, Atos won government contracts worth £400m to test whether disabled people should continue receiving disability living allowance benefits. The Cabinet Office said all contracts were "based on the best value for money for taxpayers and are subject to strict scrutiny".

The disability campaigners are being backed by UK Uncut, which hopes its tactics of peaceful occupation and canny use of social media will galvanise the wider public in action. Tony Smith, spokesperson for UK Uncut, said: "Atos are doing the government's dirty work, taking away benefits from disabled people without regard for their needs, leaving many in poverty and driving some to suicide. They are being paid millions of pounds of taxpayers' money to rip apart our welfare system."

Analysts said the company had become a whipping boy because of the tests. Rachael Stormonth, of NelsonHall analysts, said Atos had inherited the assessments when it bought a company that used to test coal miners for emphysema. "Both the amount of time Atos gets and the quality of the assessment is up to the government. They are the whipping boys here," said Stormonth.

An Atos spokesperson said: "We are proud of our association with the Paralympic Games and have provided technology and support since 2002 to help ensure their success.

"We run a number of contracts in the UK, both in the private sector and within government, and offer our customers good value for money alongside high standards of service, delivery and flexibility. In particular, Atos has been providing medical assessments to government for 13 years."

A government spokesperson said sponsorship was a matter for Games organisers, saying: "Locog and the International Paralympic Committee make all decisions on sponsorship for the Paralympics. All the partners provide vital funding without which the Games would not happen and they operate within the supplier guidelines."

"It's disappointing that a small number of organisations are protesting against sponsorship of the Paralympic Games, which is an opportunity to showcase the talents of disabled people and act as a catalyst for our sporting talents of the future."